472, MR. S. 8S. HOUGH ON THE OSCILLATIONS OF A 
become 

A() +405 =A pn +1M(#+ y)é 
= [BOQ +n) +H FIM (+7) 9 [oF (M-+7)[C+ MM (e+ 6 )]o=0 
~ =o 

= (+ Sibi 70, + 3M (8+) é]o=0 
B (Qs +) + wey Gs + AM (9 $0) 7 

C(O, +) + eM Go 0, + IM (2 + 
HELMHOLTz’s equations of vortex motion are 
Qa? 28? 
Hr er eee E= 0. 
Hence, if we put &, 7), 0), Q:, Q;, € — w each proportional to e”, and introduce, 
for brevity, the notation A’=3M (6? + y’), & 
s[atreet)a ra tard ) 
@ 
Tests each ala 











ise is Be -/ 
lc $O AWE =| 0, (4). 
By 7a NOH caeeila col 
+(C+0'-A-a)£-“[(B 4p 5=%) 0, + (B+ B)n] =0, 
qa Sg Me a ae 
ae ar tee Oa eg ee J 
03, = 0 C=o. 
Eliminating 0,, ©), € y, the period equation is 
| AL B—» | Ate DY ae? we , Rel yoy. Dy 
pe [at+oS-]. CHO —B—p =, M(A+A), C4+C—B-B | 
| —— fa\ sibert —M Cees E Vous) A EEIAU, = 
Re Apo = (ees C40'=A=A', (B4B’) LE 
Qo? nM =i 
| 0, top? Bs > 0, 
| — 28? ri 
B+? 0, 0, ay 
